Understand how categorical logic differs from propositional logic.
Learn the definitions of subject term, predicate term, copula, quantifier, quantity, and quality.
Memorize the four standard-form categorical statements.
Translations and Standard Form
Know how to translate ordinary statements into standard categorical form.
Know how to translate singular statements into standard form.
Diagramming Categorical Statements
Be able to construct a Venn diagram for any categorical statement.
Memorize the Venn diagrams for the four standard-form categorical statements.
Know how to use Venn diagrams to tell if two statements are, or are not, equivalent.
Sizing Up Categorical Statements
Understand the structure of categorical syllogisms.
Know the definition of major term, minor term, middle term, major premise, and minor premise.
Know how to check the validity of a categorical argument by drawing Venn diagrams.
Chapter summary
Every categorical statement has a subject term and a predicate term. There are four standard forms of categorical statements:
(1) universal affirmative ("All dogs are mammals");
(2) universal negative ("No dogs are mammals");
(3) particular affirmative ("Some dogs are mammals"); and
(4) particular negative (Some dogs are not mammals").
Categorical statements must be translated into standard form before you can work with them. Translating involves identifying terms and ensuring that they designate classes and determining the quantifiers. Drawing Venn diagrams is a good way to visualize categorical statements and to tell whether one statement is equivalent to another.
A categorical syllogism is an argument consisting of three categorical statements (two premises and a conclusion) that are interlinked in s structured way. The syllogism consists of a major term, minor term, and middle term. The middle term appears once in each premise. The major term appears in one premise and the conclusion, and the minor term appears in the other premise and the conclusion. You can use Venn diagrams to represent categorical statements, showing how the terms are related.
The easiest way to check the validity of a categorical syllogism is to draw a three-circle Venn diagram -- three overlapping circles with the relationship between terms graphically indicated. If, after diagramming each premise, the diagram reflects what's asserted in the conclusion, the argument is valid. If not, the argument is invalid.
Chapter 07
Chapter Objectives
Statements and Classes
Translations and Standard Form
Diagramming Categorical Statements
Sizing Up Categorical Statements
Chapter summary
Every categorical statement has a subject term and a predicate term. There are four standard forms of categorical statements:
(1) universal affirmative ("All dogs are mammals");
(2) universal negative ("No dogs are mammals");
(3) particular affirmative ("Some dogs are mammals"); and
(4) particular negative (Some dogs are not mammals").
Categorical statements must be translated into standard form before you can work with them. Translating involves identifying terms and ensuring that they designate classes and determining the quantifiers. Drawing Venn diagrams is a good way to visualize categorical statements and to tell whether one statement is equivalent to another.
A categorical syllogism is an argument consisting of three categorical statements (two premises and a conclusion) that are interlinked in s structured way. The syllogism consists of a major term, minor term, and middle term. The middle term appears once in each premise. The major term appears in one premise and the conclusion, and the minor term appears in the other premise and the conclusion. You can use Venn diagrams to represent categorical statements, showing how the terms are related.
The easiest way to check the validity of a categorical syllogism is to draw a three-circle Venn diagram -- three overlapping circles with the relationship between terms graphically indicated. If, after diagramming each premise, the diagram reflects what's asserted in the conclusion, the argument is valid. If not, the argument is invalid.